Forty years ago, the Young Vic opened its doors with a production of Scapino!, an updated Molière play starring Jim Dale. Tickets were cheap at seven-and-sixpence (the equivalent of 40p). Rock music played in the foyer. The bar served high-class hamburgers. Frank Dunlop, whose brainchild the whole project was, had set out to attract what he called "the lost generation of teenagers". And the director's guiding principle was to offer them nothing but the best. Shakespeare, Sophocles, Beckett and Genet were all part of the opening seasons alongside music-theatre from Stravinsky, Henze and the Who. And, as a dedicated European, Dunlop invited experimental companies from the continent, which occasionally landed him in hot water – not least because the Young Vic began as an offshoot of Laurence Olivier's National Theatre Company at the Old Vic.

"I remember," says Dunlop, "a highly praised and attractive Swiss company arrived to play Romeo and Juliet – mostly with no clothes on. The wife of a senior member of the National Theatre administration complained that a sportive young naked Swiss guy had sat on her knee during the performance and embraced her. This was considered an affront, not art, and a call came for the National Theatre board to censure me and possibly close us down. But Lord Chandos, chairman of the NT board, told them that, 'Mrs X should perhaps have been grateful for the experience at her time of life. Certainly I should have if a young nubile female had entertained me in such respectable circumstances. On to the rest of the agenda.'"

Heady days. Dunlop also recalls that, with the opening show of Scapino!, they were stuck for a rousing finale. So he and Jim Dale, veteran of countless Carry On movies, nipped into a local Italian restaurant and hastily improvised a song listing spag bol, tagliatelle and all the other items they could find on the menu. At a later performance of The Taming of the Shrew, in which Dale played Petruchio and Richard Gere made his theatrical debut, a somewhat chemically excited Keith Moon rose from his seat in the stalls and took a bow standing behind the star. At which point Dale blew his top and, screaming "I'll murder him", chased the intrusive Who drummer from the building.

Not every night was as exciting as this. But, when I chaired a recent event at the National Theatre to mark the Young Vic's 40th birthday, I asked what the secret was of its enduring success. David Lan, the current artistic director, summed it up best when he said "a sense of joy". That quality of joy was built into Dunlop's vision from the start. He wanted to create a theatre that was cheap, informal and democratic. He was also lucky enough to find a brilliant architect, Bill Howell, who, for the astonishingly modest sum of £60,000, designed a breezeblock building that combined elements of Greek and Elizabethan stages and the circus. The building, near Waterloo station in south London, was never intended to be more than temporary. Yet, suitably renovated, it still survives and remains as welcoming as ever.

Physical stagings, erotic tensions

Over the years, Dunlop's dream has been sustained by successive directors who have imported their own particular style. After Dunlop came Michael Bogdanov, who had a gift for highly physical stagings of popular classics such as Hiawatha. The trademark signature of David Thacker in the 80s was his passion for Ibsen, Miller and O'Neill: he directed a radical version of Ghosts, with Vanessa Redgrave and Timothy Dalton, that seethed with erotic tension, and a production of O'Neill's Anna Christie in which the late Natasha Richardson first revealed her shining talent. In the 90s, Tim Supple, first with Julia Bardsley and then flying solo, not only investigated the classic repertory, he also raised Christmas children's shows to a new level with his own terrifying production of Grimm's Fairytales. Supple describes the Young Vic as "a triumph of subsidy: an irrefutable exemplar of the madness and vandalism of the government's threatened cuts."

So where does the Young Vic stand today? Obviously, it's benefited from Steve Tompkins's refurbishment, in that it now has three performance spaces, bigger bars and an easily adjustable auditorium. David Lan, while building on the work of his predecessors, has also put his own stamp on proceedings. How would one define the last decade? By an eclectic internationalism, a fascination with music-theatre (everything from Katie Mitchell's After Dido to Annie Get Your Gun) and big community projects such as the recent The Human Comedy.

"One of my guiding principles," says Lan, "is to make this a director's theatre. It's partly a response to the provocation of the Royal Court, which is primarily a writer's theatre, and partly because I simply follow my own taste. So, when an Icelandic producer knocked on my door and suggested I take a trip to Reykjavik, that started an on-going relationship with the Vesturport company, who brought us a highly acrobatic Romeo and Juliet and have now staged a new version of Goethe's Faust. But we've also had the South African Magic Flute, a Brazilian company and major European directors such as Peter Brook, Luc Bondy and this season Patrice Chéreau. Our own work is also travelling far and wide. Kafka's Monkey, with Kathryn Hunter, is heading to Paris, Kursk is going to Australia and Richard Jones plans to take his production of The Good Soul of Szechuan to Beijing."

A socialist theatre

Lan's Young Vic also acts as a spiritual, and even physical, home to young directors. It has created an internet network in which an incredible 650 existing directors exchange information. It tracks the careers of another 60 directors to whom it offers regular classes in lighting, sound, design and working with actors. And, at any time, there are six young directors in the building who assist, read plays and do their own parallel production. "When Richard Jones did Annie Get Your Gun in the main house," says Lan, "we had a young director do her own alternative production with 25 actors in our studio space, the Clare."

But, most important of all, Lan has inherited from Supple the idea of targeting and discovering a new audience: for each production, 10% of tickets are given away free to residents of Lambeth and Southwark. For the recent Beauty Queen of Leenane, 1500 tickets were distributed over the course of 40 performances: a tribute to the work of a full-time specialist who has forged relationships with schools, libraries and just about every institution in the borough.

"I suppose the bottom line of all this," says Lan, "is that we are a socialist theatre." It's not a word we hear very often in public life these days. But it's a testament to Lan's convictions and to the inspiration he found in Jean Vilar's Théâtre National Populaire, which in 1950s France attempted to create a classless performance space and speak directly to young audiences. The intriguing thing is that it's the same ideal that animated Dunlop back in 1970. The Young Vic will always be, as Olivier said, "Frank's baby"; but the good news is that, even though it has reached middle-age, it retains the pioneering, populist instinct that gave it birth.